Assembly of reconfigurable one-dimensionalcolloidal superlattices due to a synergyof fundamental nanoscale forcesKaylie L. Younga,b, Matthew R. Jonesb,c, Jian Zhanga,b, Robert J. Macfarlanea,b, Raul Esquivel-Sirventa,d, Rikkert J. Nape,Jinsong Wuc, George C. Schatza,b, Byeongdu Leef,1, and Chad A. Mirkina,b,c,e,1

aDepartment of Chemistry, and bInternational Institute for Nanotechnology, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208;cDepartment of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, IL 60208; dInstituto de Fisica, UniversidadNacional Autonoma de Mexico, Apartado Postal 20-364, DF 01000, Mexico; eDepartment of Biomedical Engineering, Northwestern University, 2145Sheridan Road, Evanston, IL 60208; and fX-ray Science Division, Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue,Argonne, IL 60439

Contributed by Chad A. Mirkin, December 5, 2011 (sent for review September 24, 2011)

We report that triangular gold nanoprisms in the presence ofattractive depletion forces and repulsive electrostatic forces assem-ble into equilibrium one-dimensional lamellar crystals in solutionwith interparticle spacings greater than four times the thicknessof the nanoprisms. Experimental and theoretical studies reveal thatthe anomalously large d spacings of the lamellar superlattices aredue to a balance between depletion and electrostatic interactions,both of which arise from the surfactant cetyltrimethylammoniumbromide. The effects of surfactant concentration, temperature,ionic strength of the solution, and prism edge length on the latticeparameters have been investigated and provide a variety of tools forin situmodulationof these colloidal superstructures. Additionally,wedemonstrate a purification procedure based on our observations thatcan be used to efficiently separate triangular nanoprisms from sphe-rical nanoparticles formed concomitantly during their synthesis.

anisotropic ∣ tunable ∣ small angle X-ray scattering ∣ depletion interaction

The ability to form ensembles of inorganic nanoparticles with ahigh degree of control has become one of the main areas of

focus in nanoscience research (1). This interest stems from thefact that nanocrystal superlattices often exhibit electronic (2),optical (3), and magnetic (4) properties that are distinct fromboth the corresponding individual particles and the bulk solidas a result of the interactions between the excitons, surface plas-mons, or magnetic moments of the assembled particles (5).Superlattices composed of spherical building blocks have beenextensively studied, and researchers now have the ability tosynthesize a wide variety of structures (6). However, as new tech-niques are developed to synthesize high-quality anisotropic nano-particles with new physical properties that cannot be obtainedwith spheres alone, researchers are increasingly interested in therich assembly behavior of particles with reduced symmetry (7–9).Indeed, periodic arrays of these anisotropic building blocks havebeen shown to possess unique collective properties with applica-tions in various fields including plasmonics (10) and photonics(11). However, to take full advantage of these collective proper-ties, it is necessary to understand the relationship between thearchitectural parameters of the ensemble and the emergent phy-sical properties. For this purpose, it is crucial to be able to “engi-neer” the various interactions that exist between nanoparticlebuilding blocks to produce a desired structure (12, 13). The assem-bly of nanocrystals into ordered arrays can be induced via themanipulation of interparticle interactions including van der Waals(14), electrostatic (15), entropic (16–21), and through highly spe-cific biological interactions (22–24). Herein, we report the assem-bly of colloidal triangular gold nanoprisms protected by acetyltrimethylammonium bromide (CTAB) bilayer in a solutionof CTAB micelles into highly ordered 1D crystals with unexpectedstructural features that emerge from a synergy of attractive deple-

tion and repulsive electrostatic interactions. This system is uniquein that it allows access to a regime wherein several interparticleforces are of comparable strength, leading to an unusual exampleof a one-dimensional superlattice of inorganic disc-like nanostruc-tures that is stable in solution. Furthermore, these columnarassemblies are highly reconfigurable through modification of sev-eral intensive and extensive variables, providing a means to createtunable stimuli-responsive materials (18, 25).

Depletion forces are purely entropic in nature and arise whensmall, nonadsorbing molecules, such as surfactants, are added toa colloidal solution of particles (26). Two large particles of radiusR immersed in a dispersion of small particles (depletants) withradius r possess an exclusion layer whose thickness is equal tor. As the surfaces of the large particles reach a separation smallerthan the diameter of the depletant (2r), their exclusion layers be-gin to overlap and the total volume available to the depletants isincreased, thereby decreasing the free energy of the system by

Edep ¼ −nkBTΔV; [1]

where n is the number density of the depletant, kB is the Boltz-mann’s constant, T is the temperature, and ΔV is the volumegained by the overlap of exclusion layers (13). The depletionforce can also be thought of in terms of osmotic pressure: Theexclusion of the depletant from the space between the particlesresults in a local concentration gradient that produces a netosmotic pressure acting to push the particles together. Thestrength of the interaction energy is proportional to the magni-tude of the volume gained by bringing two particles together, andtherefore depletion forces are particularly attractive for assem-bling anisotropic building blocks because they can potentiallyhave a more efficient overlap of their exclusion layers comparedto spherical building blocks due to directionally dependent inter-actions (27). Additionally, depletion forces are maximized forsmooth surfaces because very little free volume is gained whentwo rough surfaces approach each other (28). This fact makesplate-like triangular gold nanoprisms an ideal structure to probedepletion force-based assembly because they are extremely ani-sotropic (aspect ratio of ca. 19) and have atomically flat triangularfaces on the top and bottom (29), allowing the strength of the

Author contributions: K.L.Y., M.R.J., B.L., and C.A.M. designed research; K.L.Y., M.R.J., J.Z.,R.J.M., J.W., and B.L. performed research; K.L.Y., M.R.J., and B.L. analyzed data; R.E.-S.,R.J.N., G.C.S., and B.L. performed theoretical calculations; and K.L.Y., M.R.J., B.L., andC.A.M. wrote the paper.

The authors declare no conflict of interest.1To whom correspondence may be addressed. E-mail: chadnano@northwestern.edu orblee@aps.anl.gov.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1119301109/-/DCSupplemental.

2240–2245 ∣ PNAS ∣ February 14, 2012 ∣ vol. 109 ∣ no. 7 www.pnas.org/cgi/doi/10.1073/pnas.1119301109

Dow

nloa

ded

by g

uest

on

Oct

ober

20,

202

1

depletion force to be maximized. Colloidal nanoprisms are highlytunable anisotropic structures that exhibit size- and shape-depen-dent plasmon resonances (30) and are predicted to exhibit uniquecollective optical properties (5, 9).

In our system, the synergy of depletion and electrostatic forcescauses triangular nanoprisms to naturally assemble into one-dimensional lamellar colloidal crystals with interparticle spacingsgreater than four times the thickness of the nanoprism buildingblocks. Forces that inherently have no directionality are made toprefer specific interaction modes via particle anisotropy, consis-tent with previous reports of directional entropic interactions(31). Both types of interactions arise from the presence of thesurfactant CTAB: In solution, the CTAB molecules form micellesthat act as depletants, driving the entropic association of prisms,whereas the presence of the CTAB bilayer leads to a positivecharge on the surface of the prisms (32, 33), causing an electro-static repulsion between them. The combination of extremelyanisotropic particles and charged depletant molecules leads tothe formation of robust crystals with interparticle spacings thatare significantly larger than the particle size, which, to the best ofour knowledge, is an unprecedented example of achieving suchlarge spacings between particles using interparticle forces alone(13). We demonstrate that the lattice parameters are reversiblytunable in situ by manipulating the balance of the forces via achange in surfactant concentration, temperature, or ionic strength.Additionally, we propose a simplified model that explains the largelamellar d spacings observed experimentally by minimizing the freeenergy of the system, taking into account the relevant interactions.Finally, we utilize the fundamental knowledge gained in this studyto develop a procedure to purify the anisotropic triangular goldnanoprisms from the spherical gold nanoparticles formed conco-mitantly during their synthesis, which has proven to be a challengeto date (29).

Results and DiscussionGold nanoprisms (henceforth also referred to as prisms) weresynthesized according to literature methods with minor modifica-tions (29) (SI Appendix). A typical synthesis produces a mixture oftriangular gold nanoprisms (thickness of 7.5� 1 nm and threecongruent edges) and spherical gold particles (SI Appendix,Fig. S1). Nanoprism edge length was varied from 40–210 nm bychanging the ratio of the gold seeds to the gold salt precursor(34). The cationic surfactant CTAB serves as the stabilizing agentin our system. CTAB forms a bilayer structure around the goldnanoprisms, with the inner layer binding to the gold surface viaits charged headgroups (32). The adsorbed bilayer has an approx-

imate thickness of 3.2 nm (35, 36) and leads to a net positivecharge on the surface of the prisms (32, 33). Because the synthesisof the prisms is carried out at a CTAB concentration of 50 mM,which is 50 times the critical micelle concentration (1 mM) (36),charged CTAB micelles are also present in solution. At a CTABconcentration of 50 mM, the fractional charge of the micelles isapproximately 0.26 (37).

Immediately after their synthesis and without further modifi-cation, the 7.5-nm-thick prisms (145-nm edge length) naturallyassemble into 1D lamellar superlattices in solution with theprisms aligned face-to-face with a center-to-center spacing (d spa-cing) of 29.9 nm (Fig. 1 A and B). These lamellar nanoprism crys-tals were characterized by small angle X-ray scattering (SAXS)using the Advanced Photon Source at Argonne National Labora-tory. The two-dimensional scattering images were radially aver-aged over all orientations to produce plots of scattered intensityIðqÞ versus scattering vector q, where q ¼ 4π sin θ∕λ. The SAXSprofile for 145-nm edge length prisms (Fig. 1D) features four re-solvable diffraction peaks at integer spacings with respect to thefirst-order peak (q ¼ 0.021, 0.042, 0.063, 0.084 Å−1), consistentwith a highly ordered lamellar structure (38, 39). Although thescattering from the spherical gold particles (form factor) canbe seen in the SAXS patterns (39), they were not found to havean effect on the formation of the lamellar nanoprism crystals and,as a result, were disregarded for the remainder of this study (SIAppendix, Fig. S2). Using the Scherrer equation (40), the crystal-lites were determined to contain a total of 10–15 prisms. Cryoe-lectron microscopy images of the nanoprism superlattices providefurther evidence of the lamellar structure (Fig. 1C). However, itis important to note that the appearance of hexagonal orderingbetween 1D nanoprism columns and the reduced interparticlespacings observed in the image are likely consequences of themicroscopy preparation procedure, as these features are not sup-ported by the SAXS data.

A d spacing of approximately 30 nm between 7.5-nm-thickprisms corresponds to a solvent layer (dw) of approximately16 nm when the CTAB bilayer on the prisms is taken into account(Fig. 1B). A 1D electron density profile ρðzÞ was derived from theSAXS data using a Fourier synthesis method to confirm the largeinterparticle spacing (39) (SI Appendix, Fig. S3). AnomalousSAXS studies at the X-ray absorption edges of Au and Br re-vealed that the majority of the Br− species are located outside ofthe lamellar superstructures, as opposed to between the nano-prisms that make up the superlattices, suggesting that the major-ity of the micelles are located outside of the lamellar crystals (SIAppendix, Fig. S4).

Fig. 1. Columnar superlattices of anisotropic gold nanoprisms. (A) Nanoprisms form 1D lamellar crystals in solution with an average of 10–15 prisms per crystal.(B) A zoomed in edge-on view of two nanoprisms within a lamellar superlattice where d is the d spacing, dw is the water region, tprism is the thickness of thenanoprism, tbCTAB is the thickness of the CTAB bilayer, and dCTAB is the diameter of the CTAB micelles. (C) Cryoscanning transmission electron microscopy imageof the lamellar crystals. The outlined region highlights an edge-on view of the nanoprism crystals. (Scale bar: 200 nm.) (D) One-dimensional SAXS profile of theas-synthesized Au nanoprisms (145-nm edge length) in solution. The sharp diffraction peaks at q ¼ 0.021, 0.042, 0.063, and 0.084 1∕Å indicate a periodiclamellar structure.

Young et al. PNAS ∣ February 14, 2012 ∣ vol. 109 ∣ no. 7 ∣ 2241

CHEM

ISTR

Y

Dow

nloa

ded

by g

uest

on

Oct

ober

20,

202

1

According to Eq. 1, bringing the nanoprisms into close proxi-mity increases the total volume available to the CTAB micelles,the depletants in this system, thereby increasing the entropy ofthe micelles and decreasing the free energy of the overall system.The length scale of traditional depletion forces that take onlyhard sphere interactions into account is determined by the sizeof the depletant (13). The CTAB micelles were determined tobe approximately 5.8 nm in diameter by small angle neutron scat-tering (SANS) at the High Flux Isotope Reactor at Oak RidgeNational Laboratory (SI Appendix, Table S1), consistent withthe literature (41). According to depletion theory, interactionsresulting from such small particles at a relatively low volume frac-tion are weak compared to the repulsive electrostatic interactionsand cannot induce assembly. However, in our system, the CTABmicelles are also charged, similar to the CTAB bilayer on the na-noprisms (32). Previous theoretical studies by Walz and Sharmaconfirm that the presence of a long-range electrostatic repulsiongreatly increases both the magnitude and range of the depletioneffect (42). We thus inferred that, in addition to the depletionattraction, and possibly a minor contribution from attractivevan der Waals interactions, a repulsive force must also be present,originating from electrostatic interactions between the CTAB-coated nanoprisms.

We have developed a simplified model that captures the fun-damental physics required to explain the large d spacings ofthe nanoprism superlattices observed with SAXS based on thehypothesis that the combination of charged prisms and chargedCTAB micelles leads to the anomalously large interparticle spa-cings. The model takes into account the competition between theattractive depletion and van der Waals interactions that favorthe formation of lamellar stacks of nanoprisms and the repulsiveelectrostatic interactions that favor the dispersion of the nano-prisms in solution.

The depletion interaction energy is based on Eq. 1. However,Eq. 1 is only valid for a very dilute system where the depletantbehaves as an ideal gas and therefore Eq. 1must be modified whenthe depletants are charged and highly concentrated (43, 44). For asystem with charged particles and depletants, the volume gain,ΔV in Eq. 1, is larger than it would be for a neutral system. Thevolume gain is larger because the effective size of the CTAB-coated nanoprisms and the CTAB micelles is increased by somefactor δmultiplied by the Debye length κ−1 (42, 45, 46). To capturethis effect, the effective sizes of the prisms (tprism;eff) and the mi-celles (dCTAB;eff) are denoted as tprism þ 2tbCTAB þ 2δprismκ

−1 anddCTAB þ 2δCTABκ

−1, respectively, where tprism is the thickness ofthe prism (7.5 nm), tbCTAB is the thickness of the CTAB bilayeron the surface of the prism (3.2 nm) (35, 36), and dCTAB is the dia-meter of the CTABmicelles (ca. 5.8 nm). For a neutral system, bothδprism and δCTAB would be zero. For our system, δprism and δCTABwere used as fitting parameters to most accurately capture the var-iation of the d spacing as a function of the CTAB concentration (45).

Additionally, the effects of the high concentration of deple-tants must be taken into account. As the concentration of thecharged CTAB micelles increases, the osmotic pressure differ-ence within the superlattices compared to the surrounding solu-tion, ΔΠ, does not increase linearly with CTAB concentration asit would for a dilute system. As a result, the higher order coeffi-cients in the virial expansion of the particle distribution functionare nonzero and need to be considered (42). To include for thiseffect, we modeled ΔΠ using the Carnahan–Starling equation ofstate (45, 47, 48) for a charged micelle system in which

ΔΠ ¼ nkBTð1þ ϕeff þ ϕ2eff − ϕ3

effÞð1 − ϕeffÞ−3; [2]

where n ¼ ðNA∕NaggÞðcCTAB-ccmcÞ, Φeff ¼ nð4∕3ÞπðdCTAB;eff∕2Þ3,NA is Avogadro’s number, Nagg is the aggregation number of themicelle (145 for 0.05 M CTAB) (37), cCTAB is the CTAB concen-tration, and ccmc is the critical micelle concentration (1 mM) (36,

45, 47). The values of dCTAB,Nagg, κ−1, and the effective charge ofthe CTAB micelles vary with CTAB concentration, temperature,and ionic strength. The values used in this work are obtained fromliterature (36, 37, 45, 47) and are summarized in the SI Appendix.For simplicity, we assumed that the CTAB micelles are sphericalwith an aggregation number that varies predictably with CTABconcentration (37). The depletion interaction energy is thereforegiven by the following expression:

Edep ¼ −ΔΠAðtprism;eff þ dCTAB;eff − dÞ; [3]

where ΔΠ is the osmotic pressure difference, A is the area of ananoprism triangular face (9;104 nm2 for 145-nm edge lengthprisms), and d is the center-to-center interparticle spacing be-tween prisms. This equation helps explain why depletion inter-actions favor assembly of anisotropic particles: The reduction infree energy of the system is proportional to the area of the par-ticle A. The prisms have large smooth faces with a large value of Aand thus feel depletion attractions at greater distances with lowdepletant concentrations compared to isotropic spherical parti-cles (27, 28). Additionally, the gain in free energy by aligning theprisms parallel, or face-to-face, is much larger than by aligningside-to-side or side-to-face (27), which is the reason the nano-prisms do not form random aggregates, but instead form periodiclamellar structures. The SAXS patterns did not reveal any order-ing of the lamellar superlattices relative to each other in solution(SI Appendix, Fig. S5). It is important to point out that the use ofexcluded volume and short-range depletion forces to assemblemicron-sized platelets is well established in the literature (27).The novelty of the current system lies in the ability to assemblenanoscale particles with interesting optical properties into colum-nar assemblies with lattice parameters significantly larger thanthe dimensions of the building blocks by taking advantage of asynergy of fundamental forces.

To calculate the electrostatic interaction energy, the solution ofthe linearized Poisson–Boltzmann equation is used assuming nocharge regulation (47). The expression can be written as

Eel ¼ εε0κφ2A

�1 − tanh

�κðd − tprism − 2tbCTABÞ

2

��; [4]

where ε is the relative permittivity of the solvent (in this case,water), ε0 is the permittivity of free space, φ is the constant po-tential at the nanoprism surface (0.035 V) (33), and κ is the in-verse Debye length, defined as ð∑iciz

2i e

2∕εε0kBTÞ1∕2 (0.372 nm−1

for 0.05 M CTAB), where ci and zi are the concentration andvalency of electrolyte i, and e is the elementary charge (49). Itshould be noted that our calculation of the Debye length takes intoaccount the dissociated micelle counterions as well as any saltsadded to change the ionic strength of the solution (e.g., NaCl).

When only electrostatic and depletion interactions are consid-ered, the free energy is minimized at d ¼ 28.8 nm (Fig. 2), whichis in good agreement with the d spacing of 29.9 nm observed withSAXS. When van der Waals interactions are included in the en-ergy minimization calculations (see SI Appendix), the free energyminimum shifts slightly to d ¼ 28.1 nm (Fig. 2). However, the mini-mum in the net interaction energy becomes deeper by approxi-mately 3.2 kBT. Thus, although van der Waals interactions havea negligible effect on the d spacing of the crystal at a CTAB volumefraction of 0.05, they do make the lamellar crystals more stable. Ifonly van der Waals and electrostatic interactions are considered,the free energy curve does not possess a minimum (Fig. 2), reinfor-cing the importance of the depletion force in this system.

In order to experimentally probe that the lamellar prism assem-bly is the result of a balance between depletion and electrostaticinteractions, four parameters were investigated—CTAB concen-tration, temperature, ionic strength, and prism edge length—tomanipulate the balance of the interactions. According to Eq. 1,

2242 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1119301109 Young et al.

Dow

nloa

ded

by g

uest

on

Oct

ober

20,

202

1

the strength of the depletion interaction can be increased via anincrease in the number density of CTAB micelles. Consequently,CTAB was incrementally added to increase the overall CTAB con-centration from the starting 0.05 to 0.30 M. As is shown in Fig. 3A,with each addition of CTAB, the diffraction peaks shifted to higherq values, indicative of a smaller d spacing between nanoprisms inthe lamellar crystals. A sixfold increase in the CTAB concentrationled to a 10-nm decrease in the d spacing (Fig. 3B), which agreeswith the values calculated using the effective size of the CTABmicelles. The addition of CTAB leads to an increase in the numberof CTAB micelles, and although the micelles are slightly larger athigher CTAB concentrations (37), they are also much closer to-gether in the solvent (SI Appendix, Table S1), increasing the netosmotic pressure that acts to bring the prisms together. Conversely,a dilution of the CTAB concentration led to an increase in d spacingand an eventual dissociation of the lamellar crystals at CTAB con-centrations of 0.04 M and below (Fig. 3C). This effect was found tobe entirely reversible: By cycling between 0.025 and 0.05 M CTAB,the diffraction peaks in the SAXS pattern disappeared and reap-peared almost instantaneously, indicating the immediate dissocia-tion and formation of the lamellar crystals, respectively.

The effect of temperature was studied by increasing the tem-perature of the colloidal nanoprisms at a constant heating rate of0.5°∕min using a Peltier device and monitoring the position of thefirst-order diffraction peak in the SAXS pattern. As the tempera-ture of the system was increased from 25 to 70 °C, the d spacingdecreased by 2.8 nm (Fig. 4). This trend is explained by consider-

ing the size of the CTAB micelles at various temperatures. Anincrease in the temperature causes a decrease in the diameterof the CTAB micelles (50), as confirmed by the SANS studies(SI Appendix, Table S1). Because the overall CTAB concentrationdoes not change, the reduction in micelle size leads to an increasein the number of CTAB micelles, which increases the osmoticpressure and acts to bring the nanoprisms closer together. Whenthe temperature-dependent size of the micelles is taken into ac-count, the calculated d spacings are in close agreement with themeasured values (Fig. 4). The temperature-dependent interpar-ticle spacing was found to be reversible without hysteresis whenthe samples were heated and cooled between 25 and 70 °C for twoconsecutive cycles (Fig. 4).

To manipulate the repulsive electrostatic interactions that existbetween the positively charged gold nanoprisms, the ionicstrength of the solution was increased via the addition of NaCl,which decreased the Debye length. As NaCl was incrementallybrought to a final concentration of 0.1 M, the SAXS patternsmaintained their sharp diffraction peaks consistent with lamellarordering, but the d spacing decreased by 12.2 nm, from 29.1 to16.9 nm (Fig. 5A). By decreasing the strength of the repulsiveelectrostatic interaction, the attractive interactions become rela-tively stronger and decrease the prism-to-prism distance withinthe 1D crystals, although the depletion interaction also decreasesdue to the reduction of the effective size of the prisms and mi-celles. The addition of salt may slightly increase the physical sizeof the CTABmicelles, but the effect is known to be minimal whenchloride-based salts are used compared to bromide-based salts(50). Although the calculated values deviate slightly at higher saltconcentrations, they do capture the general trend of the experi-mental data (Fig. 5A). As with CTAB concentration and tempera-ture, the effect of increased ionic strength on the d spacing isreversible. By centrifuging the prisms at 2;100 × g for 15 s andredispersing the pellet in 0.05 M CTAB, the original d spacingis restored and is reversible over several cycles (Fig. 5B).

Interestingly, manipulation of the ionic strength of the solutionallows nanoprisms of varied edge lengths to be assembled intolamellar superlattices. As synthesized, prisms with small edgelengths do not naturally assemble into 1D lamellar crystals in so-lution. Whereas the SAXS patterns of prisms with edge lengthsgreater than 145 nm possess four evenly spaced diffraction peaks,those with edge lengths smaller than 120 nm do not (SI Appendix,Fig. S6). The reason for this discrepancy is that, for smallerprisms, the free energy at the minimum is not deep enough toovercome thermal energy (SI Appendix, Fig. S7). Our model sug-gests that a reduction of the electrostatic interaction will lowerthe net potential energy at the minimum, thereby leading tofavorable formation of lamellar superlattices. To reduce the elec-

Fig. 2. The interaction free energy (in units of kBT ) between two nano-prisms within a lamellar superlattice in a solution of 0.05 M CTAB takinginto account the various interparticle interactions. EvdW, Eel, and Edep arevan der Waals, electrostatic, and depletion interaction energies, respectively.Whereas Eel þ Edep (red) and EvdW þ Eel þ Edep (green) possess a minimum,EvdW þ Eel (blue) does not.

Fig. 3. The effect of CTAB concentration on the d spacing of the lamellar superlattices. (A) One-dimensional SAXS profiles of the 145-nm edge length na-noprism samples as the CTAB concentration is increased from 0.05 M (Bottom) to 0.30 M (Top). The diffraction peaks shift to larger q values, indicating that theinterparticle spacing decreases with increasing CTAB concentration. (B) Plot showing the measured (blue circles) and calculated (red squares) d spacing as afunction of CTAB concentration. (C) One-dimensional SAXS profiles of the 145-nm edge length nanoprism samples as the CTAB concentration is diluted from0.05 M (Top) to 0.02 M (Bottom). The diffraction peaks disappear at CTAB concentrations of 0.04 M and below, indicating that the nanoprisms no longer formlamellar superlattices. The arrows indicate the positions of the diffraction peaks.

Young et al. PNAS ∣ February 14, 2012 ∣ vol. 109 ∣ no. 7 ∣ 2243

CHEM

ISTR

Y

Dow

nloa

ded

by g

uest

on

Oct

ober

20,

202

1

trostatic interaction, we decreased the Debye length by addingNaCl to the nanoprism solutions. Triangular nanoprisms withedge lengths of 120, 98, and 80 nm assembled into ordered lamel-lar superstructures when NaCl was added and brought to concen-trations of 0.05, 0.10, and 0.15 M, respectively (SI Appendix,Fig. S8). The smaller the edge length of the prism, the more saltthat was needed to overcome the electrostatic interaction and in-duce assembly, confirming that the depletion interaction is rela-tively weaker for smaller prisms.

Once a fundamental understanding of the role of the depletioninteractions and electrostatic interactions in the assembly of na-noprisms was achieved, the knowledge was applied to develop apurification procedure for the triangular gold nanoprism synth-esis. The synthesis developed by Millstone et al. (29) producesboth triangular nanoprisms and spherical particles that are diffi-cult to separate, particularly for prisms with small edge lengths.However, by selectively inducing the prisms to assemble into 1Dlamellar superlattices through the addition of NaCl, they can beremoved from solution using centrifugation and resuspended in0.05 M CTAB to create highly pure colloidal solutions of nano-prisms. As mentioned above, smaller edge length nanoprismsrequire a greater amount of NaCl to induce their ordering intolamellar crystals for purification. To purify nanoprisms in 0.05 MCTAB solutions with edge lengths of 120, 100, 80, 60, and 40 nm,NaCl was added to concentrations of 0.2, 0.2, 0.4, 0.4, and 0.8 M,respectively. After 1 h, the samples were centrifuged at 2;100 × gfor 15 s. The supernatant was removed and the pellet containingthe assembled prisms was resuspended in a solution of 0.05 M

CTAB. In the absence of NaCl, the nanoprisms no longer formlamellar crystals and instead redisperse in solution.

UV-visible near-infrared (UV-vis-NIR) spectroscopy was usedto confirm that the triangular nanoprisms were purified fromthe spherical nanoparticles. The UV-vis-NIR spectrum of anas-synthesized solution of gold nanoprisms contains two primaryplasmon resonances: one at approximately 530 nm due to thespherical nanoparticles and another between 700 and 1,300 nm(exact position depends on edge length) due to the nanoprisms(29) (SI Appendix, Fig. S9). The dipole plasmon resonance peakblue-shifts for smaller edge length prisms (51). After purification,the UV-vis-NIR spectra of the samples no longer contain a peakaround 530 nm from the dipole resonance of spherical goldparticles, indicating spectroscopically pure samples of gold nano-prisms (Fig. 6). Although NaCl has been used to separate goldnanoplates in previous works, the separation effect was attributedto differences in the electrostatic-based aggregation of nanoplatesand nanospheres (34). Additionally, the separation procedure took6 h and resulted in severe etching of the nanoplates. Other meth-ods using short-range depletion forces, coupled with gravitationalcreaming, have been shown to separate microdisks from micro-spheres in the past, but generally require several separation stepsto achieve significant purity and can take several days (27). In ourcase, purification can be achieved in as little as 1 h and does notdisrupt the original geometry of the triangular prisms, which is par-ticularly important when studying their optical properties, as theyare very sensitive to shape and tip sharpness (52).

ConclusionsUnderstanding the interparticle interactions that control the as-sembly of anisotropic nanostructures is essential for the design ofsuperlattices of these structures with unique collective properties.

Fig. 4. Plot of d spacing as a function of temperature for two consecutiveheating (red circles) and cooling (blue circles) cycles showing the reversibilityof the temperature-dependent d spacing of the lamellar superlattices. Thetemperature was cycled between 25 and 70 °C at a constant heating/coolingrate of 0.5 °C∕min. The black line in the first heating cycle represents the cal-culated d spacings as a function of temperature (see SI Appendix for details).

Fig. 5. The effect of ionic strength on the d spacing of the nanoprism superlattices. (A) Plot showing the measured (blue circles) and calculated (red squares) dspacing as a function of NaCl concentration. (B) Plot showing the reversibility of the effect of adding NaCl to the 145-nm edge length nanoprism samples. As theNaCl concentration is cycled three times between 0 and 0.05 M, the d spacing changes from approximately 30 nm to about 20 nm.

Fig. 6. Normalized UV-vis-NIR spectra of purified nanoprisms with edgelengths of 40, 60, 80, 100, and 120 nm. The absence of a peak around530 nm, indicative of the presence of spherical gold nanoparticles, shows thatthe nanoprisms are spectroscopically pure.

2244 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1119301109 Young et al.

Dow

nloa

ded

by g

uest

on

Oct

ober

20,

202

1

In this work, we have shown that depletion forces acting insynergy with electrostatic forces are a powerful tool for assemblingnanoscale anisotropic particles with interparticle spacings on theorder of or larger than the dimensions of the nanoparticle buildingblocks. Using highly anisotropic nanoprisms in a solution of CTABmicelles, we were able to access a regime wherein two fundamentalforces are of comparable strength, leading to unique one-dimen-sional superlattice structures which are, themselves, stable colloids.We have shown, both experimentally and theoretically, that theanomalously large d spacings of the lamellar superlattices are theresult of an equilibrium between attractive depletion and van derWaals forces and repulsive electrostatic forces.We have also shownthat the lattice parameters of the lamellar crystals are reversiblytunable between 17 and 30 nm, almost a factor of two, simplyby changing the concentration of the CTAB surfactant, the tem-perature, and/or the ionic strength of the solution. Finally, by in-ducing the lamellar ordering of gold nanoprisms in solution, wehave developed a methodology to efficiently separate nanoprismsfrom spherical nanoparticles formed concomitantly during synth-esis. The stimuli-responsive behavior of the nanoprism superlat-tices suggests that this method of assembling nanoscale colloids

could potentially be useful for reconfigurable materials that arecapable of changing their properties in response to several inten-sive and extensive variables. Furthermore, because depletion-force-based assembly of anisotropic particles requires only chargedparticles and a nonadsorbing charged depletant molecule, thismethod should be applicable to a wide range of particles with ex-tended flat faces, independent of particle composition.

ACKNOWLEDGMENTS. K.L.Y. acknowledgesDr. Ken Littrell atOakRidgeNationalLaboratory for assistance with SANS studies. C.A.M and G.C.S. acknowledge theDepartment of Energy Office (DOE Award DE-SC0000989) for support throughthe Northwestern University Nonequilibrium Energy Research Center. C.A.M. isalso grateful for a National Security Science and Engineering Faculty Fellowshipfrom the Department of Defense. K.L.Y. acknowledges the National ScienceFoundation and the National Defense Science and Engineering Graduate Re-search Fellowships. M.R.J. and R.J.M. acknowledge Northwestern Universityfor Ryan Fellowships. R.E.-S. acknowledges Dirección General Asuntos del Per-sonal Académico-Universidad Nacional Autónoma de México, Consejo Nacionalde Ciencia y Tecnologia Project 82474. Use of the Advanced Photon Source wassupported by the Office of Basic Energy Sciences, US DOE under Contract DE-AC02-06CH11357. The transmission electronmicroscopy work was carried out inthe Electron Probe Instrumentation Center facility of Northwestern UniversityAtomic and Nanoscale Characterization Experimental Center.

1. Jones MR, Osberg KD, Macfarlane RJ, Langille MR, Mirkin CA (2011) Templatedtechniques for the synthesis and assembly of plasmonic nanostructures. Chem Rev111:3736–3827.

2. Urban JJ, Talapin DV, Shevchenko EV, Kagan CR, Murray CB (2007) Synergism in binarynanocrystal superlattices leads to enhanced p-type conductivity in self-assembledPbTe/Ag2Te thin films. Nat Mater 6:115–121.

3. Tao A, Sinsermsuksakul P, Yang P (2007) Tunable plasmonic lattices of silver nano-crystals. Nat Nanotechnol 2:435–440.

4. Black CT, Murray CB, Sandstrom RL, Sun S (2000) Spin-dependent tunneling in self-assembled cobalt-nanocrystal superlattices. Science 290:1131–1134.

5. Nie ZH, Petukhova A, Kumacheva E (2010) Properties and emerging applicationsof self-assembled structures made from inorganic nanoparticles. Nat Nanotechnol5:15–25.

6. Shevchenko EV, Talapin DV, Kotov NA, O’Brien S, Murray CB (2006) Structural diversityin binary nanoparticle superlattices. Nature 439:55–59.

7. Jones MR, et al. (2010) DNA-nanoparticle superlattices formed from anisotropic build-ing blocks. Nat Mater 9:913–917.

8. Huang T, Zhao Q, Xiao J, Qi L (2010) Controllable self-assembly of PbS nanostars intoordered structures: Close-packed arrays and patterned arrays. ACS Nano 4:4707–4716.

9. Glotzer SC, Solomon MJ (2007) Anisotropy of building blocks and their assembly intocomplex structures. Nat Mater 6:557–562.

10. Tao AR, Ceperley DP, Sinsermsuksakul P, Neureuther AR, Yang P (2008) Self-organizedsilver nanoparticles for three-dimensional plasmonic crystals. Nano Lett 8:4033–4038.

11. Grzelczak M, Vermant J, Furst EM, Liz-Marzan LM (2010) Directed self-assembly ofnanoparticles. ACS Nano 4:3591–3605.

12. Min Y, Akbulut M, Kristiansen K, Golan Y, Israelachvili J (2008) The role of interparticleand external forces in nanoparticle assembly. Nat Mater 7:527–538.

13. Bishop KJM,Wilmer CE, Soh S, Grzybowski BA (2009) Nanoscale forces and their uses inself-assembly. Small 5:1600–1630.

14. Murray CB, Kagan CR, Bawendi MG (1995) Self-organization of CdSe nanocrystallitesinto three-dimensional quantum dot superlattices. Science 270:1335–1338.

15. Kalsin AM, et al. (2006) Electrostatic self-assembly of binary nanoparticle crystals witha diamond-like lattice. Science 312:420–424.

16. Redl FX, Cho KS, Murray CB, O’Brien S (2003) Three-dimensional binary superlattices ofmagnetic nanocrystals and semiconductor quantum dots. Nature 423:968–971.

17. Smith DK, Goodfellow B, Smilgies D-M, Korgel BA (2009) Self-assembled simplehexagonal AB2 binary nanocrystal superlattices: SEM, GISAXS, andDefects. J Am ChemSoc 131:3281–3290.

18. Sacanna S, Irvine WTM, Chaikin PM, Pine DJ (2010) Lock and key colloids. Nature464:575–578.

19. Baranov D, et al. (2010) Assembly of colloidal semiconductor nanorods in solution bydepletion attraction. Nano Lett 10:743–749.

20. Zanella M, et al. (2011) Assembly of shape-controlled nanocrystals by depletion attrac-tion. Chem Commun 47:203–205.

21. Barry E, Dogic Z (2010) Entropy driven self-assembly of nonamphiphilic colloidal mem-branes. Proc Natl Acad Sci USA 107:10348–10353.

22. Park SY, et al. (2008) DNA-programmable nanoparticle crystallization. Nature451:553–556.

23. Nykypanchuk D, Maye MM, van der Lelie D, Gang O (2008) DNA-guided crystallizationof colloidal nanoparticles. Nature 451:549–552.

24. Macfarlane RJ, et al. (2010) Establishing the design rules for DNA-mediated program-mable colloidal crystallization. Angew Chem Int Ed Engl 49:4589–4592.

25. Solomon MJ (2010) Materials science: Reconfigurable colloids. Nature 464:496–498.26. Asakura S, Oosawa F (1954) Interaction between two bodies immersed in a solution of

macromolecules. J Chem Phys 22:1255–1256.27. Mason TG (2002) Osmotically driven shape-dependent colloidal separations. Phys Rev

E Stat Nonlin Soft Matter Phys 66:060402.

28. Zhao K, Mason TG (2007) Directing colloidal self-assembly through roughness-controlled depletion attractions. Phys Rev Lett 99:268301.

29. Millstone JE, et al. (2005) Observation of a quadrupole plasmon mode for a colloidalsolution of gold nanoprisms. J Am Chem Soc 127:5312–5313.

30. Millstone JE, Hurst SJ, Metraux GS, Cutler JI, Mirkin CA (2009) Colloidal gold and silvertriangular nanoprisms. Small 5:646–664.

31. Damasceno PF, Engel M, Glotzer SC (2011) Crystalline assemblies and densest packingsof a family of truncated tetrahedra and the role of directional entropic forces. ACSNano, 10.1021/nn204012y.

32. Nikoobakht B, El-Sayed MA (2001) Evidence for bilayer assembly of cationic surfac-tants on the surface of gold nanorods. Langmuir 17:6368–6374.

33. Walker DA, Browne KP, Kowalczyk B, Grzybowski BA (2010) Self-assembly of nano-triangle superlattices facilitated by repulsive electrostatic interactions. Angew ChemInt Ed Engl 49:6760–6763.

34. Fan X, et al. (2010) Size-controlled growth of colloidal gold nanoplates and theirhigh-purity acquisition. Nanotechnology 21:105602.

35. Alkilany AM, Frey RL, Ferry JL, Murphy CJ (2008) Gold nanorods as nanoadmi-celles: 1-Naphthol partitioning into a nanorod-bound surfactant bilayer. Langmuir24:10235–10239.

36. Pashley RM, McGuiggan PM, Horn RG, Ninham BW (1988) Forces between bilayersof cetyltrimethylammonium bromide in micellar solutions. J Colloid Interface Sci126:569–578.

37. Aswal VK, Goyal PS (2003) Role of different counterions and size of micelle in concen-tration dependence micellar structure of ionic surfactants. Chem Phys Lett 368:59–65.

38. Lee B, FirestoneMA (2008) Electron density mapping of triblock copolymers associatedwith model biomembranes: Insights into conformational states and effect on bilayerstructure. Biomacromolecules 9:1541–1550.

39. Roe RJ (2000) Methods of X-Ray and Neutron Scattering in Polymer Science (OxfordUniv Press, New York), pp 155–209.

40. Cullity BD, Stock SR (2001) Elements of X-Ray Diffraction (Prentice Hall, EnglewoodCliffs, NJ), 3rd Ed, pp 167–171.

41. Park K, Koerner H, Vaia RA (2010) Depletion-induced shape and size selection of goldnanoparticles. Nano Lett 10:1433–1439.

42. Walz JY, Sharma A (1994) Effect of long-range interactions on the depletion forcebetween colloidal particles. J Colloid Interface Sci 168:485–496.

43. Bibette J, Roux D, Pouligny B (1992) Creaming of emulsions: The role of depletionforces induced by surfactant. J Phys II 2:401–424.

44. Amos DA, Markels JH, Lynn S, Radke CJ (1998) Osmotic pressure and interparticle in-teractions in ionic micellar surfactant solutions. J Phys Chem B 102:2739–2753.

45. Iracki TD, Beltran-Villegas DJ, Eichmann SL, Bevan MA (2010) Charged micelle deple-tion attraction and interfacial colloidal phase behavior. Langmuir 26:18710–18717.

46. Fraden S, Maret G, Caspar DLD, Meyer RB (1989) Isotropic-nematic phase transitionand angular correlations in isotropic suspensions of tobaccomosaic virus. Phys Rev Lett63:2068–2071.

47. Hunter RJ (2001) Foundations of Colloid Science (Oxford Univ Press, New York),pp 594–598.

48. Carnahan NF, Starling KE (1969) Equation of state for nonattracting rigid spheres.J Chem Phys 51:635–636.

49. Israelachvili J (2011) Intermolecular and Surface Forces (Elsevier, Burlington, MA), 3rdEd, pp 309–314.

50. Aswal VK, Goyal PS (2003) Selective counterion condensation in ionic micellar solu-tions. Phys Rev E Stat Nonlin Soft Matter Phys 67:051401.

51. Shuford KL, Ratner MA, Schatz GC (2005) Multipolar excitation in triangular nano-prisms. J Chem Phys 123:114713.

52. Kelly KL, Coronado E, Zhao LL, Schatz GC (2003) The optical properties of metalnanoparticles: The influence of size, shape, and dielectric environment. J Phys ChemB 107:668–677.

Young et al. PNAS ∣ February 14, 2012 ∣ vol. 109 ∣ no. 7 ∣ 2245

CHEM

ISTR

Y

Dow

nloa

ded

by g

uest

on

Oct

ober

20,

202

1